# Punching Shear Calculator

A column punching through a slab is a race between the perimeter ring and the load.

- Page: https://jianzhujisuan.com/en/punching-shear
- Category: Structural Design (https://jianzhujisuan.com/en/c/structural-design)
- Chinese version: https://jianzhujisuan.com/zh/punching-shear.md
- Data checked: 2026-10-25

## Quick result

With the default inputs (Column width a 400 mm, Column depth b 400 mm, Effective depth d 200 mm, Concrete strength fck 30 MPa, Tension reinforcement ρ 1.0%, Column reaction N 500 kN): **Punching resistance 613 kN**

## Inputs

| Parameter | Type | Default | Unit | Note |
|---|---|---|---|---|
| Column width a | number | 400 | mm |  |
| Column depth b | number | 400 | mm |  |
| Effective depth d | number | 200 | mm |  |
| Concrete strength fck | number | 30 | MPa |  |
| Tension reinforcement ρ | number | 1.0 | % |  |
| Column reaction N | number | 500 | kN |  |

## Formula

- **Size effect**: k = 1 + √(200/d) ≤ 2.0
- **Punching stress**: vRd,c = 0.12·k·(100ρ·fck)^(1/3) (MPa)
- **Minimum**: vmin = 0.035·k^1.5·√fck; use max(vRd,c, vmin)
- **Critical perimeter**: u1 = 2(a + b) + 4πd
- **Resistance**: VRd,c = vRd,c·u1·d
- **Utilisation**: η = N / VRd,c
- **With links**: VRd,cs = 0.75·vRd,c·u1·d + 1.5(d/sr)·Asw·fywd

## Worked example

400×400 mm column, 200 mm effective depth, C30, 1.0% reinforcement, 500 kN reaction: k 2.0, vRd,c 0.746 MPa, critical perimeter 4113 mm, 613 kN resistance, 82% utilisation and no shear reinforcement required.

## Questions

### How do I check punching shear?

Three steps. Work out the critical perimeter, u1 = 2(a + b) + 4πd, located 2d from the column face. Work out the punching stress, vRd,c = 0.12 k (100 rho fck)^(1/3) with k = 1 + √(200/d) capped at 2.0. Multiply for the resistance, VRd,c, and compare with the column reaction. A 400×400 column with d 200, C30 and 1% steel gives u1 4113 mm, 0.746 MPa and 613 kN; a 500 kN reaction is 82% utilised and fine. Above 613 kN you need links or a drop panel.

### Is it better to thicken the slab or raise the concrete grade?

Thicken the slab. Depth appears three times — in the size factor k, inside the perimeter u1 and again as a multiplier — but k = 1 + sqrt(200/d) falls as d grows and cancels part of it, so the real exponent is about 1.5 to 1.8 rather than 3. On this 400×400 column at C30 and 1% steel, going from d 200 to 240, 20% more depth, lifts capacity from 613 to 790 kN, roughly 29% rather than 40%. Concrete strength only enters as a cube root: C30 to C50 is 19%. On cost, extra depth is a small concrete increment while two grades up is a real price step per cubic metre, so adjust thickness first, then a local drop panel, and only then shear links, which are expensive to place and easy to omit.

## Related tools

- [Wind Load Calculator](https://jianzhujisuan.com/en/wind-load): Pressure goes with velocity squared; height enters through the exposure power law.
- [Snow Load Calculator](https://jianzhujisuan.com/en/snow-load): Steeper roofs hold less; above 60 degrees the shape coefficient is zero — but not at valleys and parapets.
- [Seismic Base Shear Calculator](https://jianzhujisuan.com/en/seismic-base-shear): Estimate the period, get the coefficient, multiply by seismic weight.
- [Bolt Capacity Calculator](https://jianzhujisuan.com/en/bolt-capacity): Shear or bearing, whichever is lower, governs — above 9 mm plate it is usually shear.

---

Generated by BuildCalc. All calculations run in your browser; no data is uploaded. Formulas follow national standards and common trade practice; local codes govern.